I used to own rats! I owned two. Goat & Moose. Goat was an agouti hooded and Moose the most darling little champagne hooded. I bought them from a breeder that sold out of a pet store. I should've known better because Goat was beset with rabies shortly after I got him, and Moose had very bad myco that killed him. :/ Moose would cuddle against my neck and sit on my shoulder. I even had a little shoulder pad I made for him to sit on. He liked sitting there all the way until the end, even when he was very sick. And Goat loved to swim - he would jump between little floating toys in the tub and just have a blast in the water.
I didn't get any more rats after those two but I still get very upset when people call them 'pests' and I'm vehemently against sticky or snap traps. Just barbaric.

Do you know about yoghurt drops? Rats love them, and honestly so do I. I totally tried one and I would eat a whole pack if I could.

My students have those! (I work with infants) and I hear rats got nuts for them! Also good for their digestive track.
I recently made them some home-made food that they absolutely love! Way over the store-bought stuff, and better for them!
My guys were feeders, so mass-produced generic rats. Still, big fat lovers!
I'll have to make a shoulder rest as well! That's a great idea. I have broad shoulders, but I'm not very thick so its pretty unstable for them up there.